Sharp Conditions on Global Existence and Non-Global Existence of Solutions of Cauchy Problem for 1D Generalized Boussinesq Equations. (Journal of Partial Differential Equations, 2017)
This paper consider the Cauchy problemfor a class of 1Dgeneralized Boussinesq equations utt-uxx-uxxtt+uxxxx+uxxxxtt= f(u)xx. By utilizing the potential well method and giving some conditions on f(u), we obtain the invariance of some sets and obtain the threshold result of global existence and nonexistence of solutions.